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cosh(2.r) - 1 6. (a) Show that sinh (r) %3D 2

cosh(2.r) - 1 6. (a) Show that sinh (r) %3D 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6. (a) Show that sinh (r) = cosh(2.r) – 1 2 (b) Find the nth term of the following sequence {1,8, 10, 26, 46, -..} for all n 2 1. (c) Define both absolute convergence and conditional convergence of a series. 7. (a) Given a,+1 = 2a, + an-1 and b+1 = 2b, + bn-1 for n 2 1, with ao = a1 = 1 and bo = 0, bị = 1. It can be shown that (1+ v2)" = an + b, V2, Vn 2 0. Hence, prove %3D !! that a - b = (-1)". 2 - VA-x (b) i) Compute lim ii) Hence prove the limit in i) above by e-d definition.
Transcribed Image Text:6. (a) Show that sinh (r) = cosh(2.r) – 1 2 (b) Find the nth term of the following sequence {1,8, 10, 26, 46, -..} for all n 2 1. (c) Define both absolute convergence and conditional convergence of a series. 7. (a) Given a,+1 = 2a, + an-1 and b+1 = 2b, + bn-1 for n 2 1, with ao = a1 = 1 and bo = 0, bị = 1. It can be shown that (1+ v2)" = an + b, V2, Vn 2 0. Hence, prove %3D !! that a - b = (-1)". 2 - VA-x (b) i) Compute lim ii) Hence prove the limit in i) above by e-d definition.
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